It is important to read this quote in the context of the novel and in particular of the chapter in which it is found. This quote is from Chapter 12, which is when Katniss hides in a tree as the Careers are below her and discovers that Peeta is amongst them. Also, during this time, they kill another tribute nearby who has been foolish enough to light a fire. Now that day has come, and the Careers have moved on, Katniss checks her snares and finds that she has caught a rabbit. However, she knows from experience that she cannot eat rabbit raw, and she is also endangering herself is she lights a fire, as the other tribute discovered when it led the Careers straight to her. This is why Katniss thinks of the dead tribute, as it allows her to be able to cook her meat without having to light a fire:

I hurry back to her camp. Sure enough, the coals of her dying fire are still hot. I cut up the rabbit, fashion a spit out of branches, and set it over the coals.

The quote therefore is important because it shows the thinking of Katniss and reveals how she manages to cook her raw meat so she can eat it without getting sick, whilst at the same time not running the risk of lighting the fire and therefore revealing her location to the Careers, risking being killed.